Some Hermite–Hadamard type inequalities for GAs-convex functions in the fourth sense

Baidar A. W., KUNT M.

Mathematical Methods in the Applied Sciences, vol.46, no.5, pp.5466-5482, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 5
  • Publication Date: 2023
  • Doi Number: 10.1002/mma.8846
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.5466-5482
  • Keywords: convex function, GA-s-convex function, Hermite-Hadamard inequality, Holder inequality, Holder-Iscan inequality, improved power-mean inequality
  • Karadeniz Technical University Affiliated: Yes

Abstract

© 2022 John Wiley & Sons, Ltd.In the present manuscript, we define the concept of (Formula presented.) - (Formula presented.) -convex functions in the fourth sense. We obtain the Hermite–Hadamard inequality for the newly introduced class of functions. We also establish some inequalities of the Hermite–Hadamard type for functions whose first derivative in absolute value at certain powers is a (Formula presented.) - (Formula presented.) -convex function in the fourth sense. In the last, some applications to special means of real numbers are given.